Updated: 2/21/2019

Statistical Hypotheses and Error

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Hypotheses
  • Null Hypothesis (H0)
    • Hypothesis of no difference
      • i.e. There is no link between disease and risk factor
  • Alternative Hypothesis (H1)
    • Hypothesis of difference
      • i.e. There is a link between disease and risk factor
Type I error (False positive)
  • Stating there is an association when none exits
    • incorrectly rejecting null hypothesis
  • α = probability of type I error
  • p = probability that results as or more extreme than those of the study would be observed if the null hypothesis were true 
    • General rule of thumb is that statistical significance is reached if p < 0.05
Type II error (False negative)
  • Stating there is no effect when an effect exists 
    • Incorrectly accepting null hypothesis 
  • β = probability of type II error
Power (True Positive)
  • Probability of correctly rejecting null hypothesis
    • Power = 1 - β
  • Power depends on
    • Sample size
      • Increasing sample size increases power
    • Size of expected effect
      • Increasing effect size increases power
True Negative
  • Probability of correctly accepting null hypothesis
 

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Questions (5)
Lab Values
Blood, Plasma, Serum Reference Range
ALT 8-20 U/L
Amylase, serum 25-125 U/L
AST 8-20 U/L
Bilirubin, serum (adult) Total // Direct 0.1-1.0 mg/dL // 0.0-0.3 mg/dL
Calcium, serum (Ca2+) 8.4-10.2 mg/dL
Cholesterol, serum Rec: < 200 mg/dL
Cortisol, serum 0800 h: 5-23 μg/dL //1600 h:
3-15 μg/dL
2000 h: ≤ 50% of 0800 h
Creatine kinase, serum Male: 25-90 U/L
Female: 10-70 U/L
Creatinine, serum 0.6-1.2 mg/dL
Electrolytes, serum  
Sodium (Na+) 136-145 mEq/L
Chloride (Cl-) 95-105 mEq/L
Potassium (K+) 3.5-5.0 mEq/L
Bicarbonate (HCO3-) 22-28 mEq/L
Magnesium (Mg2+) 1.5-2.0 mEq/L
Estriol, total, serum (in pregnancy)  
24-28 wks // 32-36 wks 30-170 ng/mL // 60-280 ng/mL
28-32 wk // 36-40 wks 40-220 ng/mL // 80-350 ng/mL
Ferritin, serum Male: 15-200 ng/mL
Female: 12-150 ng/mL
Follicle-stimulating hormone, serum/plasma Male: 4-25 mIU/mL
Female: premenopause: 4-30 mIU/mL
midcycle peak: 10-90 mIU/mL
postmenopause: 40-250
pH 7.35-7.45
PCO2 33-45 mmHg
PO2 75-105 mmHg
Glucose, serum Fasting: 70-110 mg/dL
2-h postprandial:<120 mg/dL
Growth hormone - arginine stimulation Fasting: <5 ng/mL
Provocative stimuli: > 7ng/mL
Immunoglobulins, serum  
IgA 76-390 mg/dL
IgE 0-380 IU/mL
IgG 650-1500 mg/dL
IgM 40-345 mg/dL
Iron 50-170 μg/dL
Lactate dehydrogenase, serum 45-90 U/L
Luteinizing hormone, serum/plasma Male: 6-23 mIU/mL
Female: follicular phase: 5-30 mIU/mL
midcycle: 75-150 mIU/mL
postmenopause 30-200 mIU/mL
Osmolality, serum 275-295 mOsmol/kd H2O
Parathyroid hormone, serume, N-terminal 230-630 pg/mL
Phosphatase (alkaline), serum (p-NPP at 30° C) 20-70 U/L
Phosphorus (inorganic), serum 3.0-4.5 mg/dL
Prolactin, serum (hPRL) < 20 ng/mL
Proteins, serum  
Total (recumbent) 6.0-7.8 g/dL
Albumin 3.5-5.5 g/dL
Globulin 2.3-3.5 g/dL
Thyroid-stimulating hormone, serum or plasma .5-5.0 μU/mL
Thyroidal iodine (123I) uptake 8%-30% of administered dose/24h
Thyroxine (T4), serum 5-12 μg/dL
Triglycerides, serum 35-160 mg/dL
Triiodothyronine (T3), serum (RIA) 115-190 ng/dL
Triiodothyronine (T3) resin uptake 25%-35%
Urea nitrogen, serum 7-18 mg/dL
Uric acid, serum 3.0-8.2 mg/dL
Hematologic Reference Range
Bleeding time 2-7 minutes
Erythrocyte count Male: 4.3-5.9 million/mm3
Female: 3.5-5.5 million mm3
Erythrocyte sedimentation rate (Westergren) Male: 0-15 mm/h
Female: 0-20 mm/h
Hematocrit Male: 41%-53%
Female: 36%-46%
Hemoglobin A1c ≤ 6 %
Hemoglobin, blood Male: 13.5-17.5 g/dL
Female: 12.0-16.0 g/dL
Hemoglobin, plasma 1-4 mg/dL
Leukocyte count and differential  
Leukocyte count 4,500-11,000/mm3
Segmented neutrophils 54%-62%
Bands 3%-5%
Eosinophils 1%-3%
Basophils 0%-0.75%
Lymphocytes 25%-33%
Monocytes 3%-7%
Mean corpuscular hemoglobin 25.4-34.6 pg/cell
Mean corpuscular hemoglobin concentration 31%-36% Hb/cell
Mean corpuscular volume 80-100 μm3
Partial thromboplastin time (activated) 25-40 seconds
Platelet count 150,000-400,000/mm3
Prothrombin time 11-15 seconds
Reticulocyte count 0.5%-1.5% of red cells
Thrombin time < 2 seconds deviation from control
Volume  
Plasma Male: 25-43 mL/kg
Female: 28-45 mL/kg
Red cell Male: 20-36 mL/kg
Female: 19-31 mL/kg
Cerebrospinal Fluid Reference Range
Cell count 0-5/mm3
Chloride 118-132 mEq/L
Gamma globulin 3%-12% total proteins
Glucose 40-70 mg/dL
Pressure 70-180 mm H2O
Proteins, total < 40 mg/dL
Sweat Reference Range
Chloride 0-35 mmol/L
Urine  
Calcium 100-300 mg/24 h
Chloride Varies with intake
Creatinine clearance Male: 97-137 mL/min
Female: 88-128 mL/min
Estriol, total (in pregnancy)  
30 wks 6-18 mg/24 h
35 wks 9-28 mg/24 h
40 wks 13-42 mg/24 h
17-Hydroxycorticosteroids Male: 3.0-10.0 mg/24 h
Female: 2.0-8.0 mg/24 h
17-Ketosteroids, total Male: 8-20 mg/24 h
Female: 6-15 mg/24 h
Osmolality 50-1400 mOsmol/kg H2O
Oxalate 8-40 μg/mL
Potassium Varies with diet
Proteins, total < 150 mg/24 h
Sodium Varies with diet
Uric acid Varies with diet
Body Mass Index (BMI) Adult: 19-25 kg/m2
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(M1.ST.20) You are conducting a study comparing the efficacy of two different statin medications. Two groups are placed on different statin medications, statin A and statin B. Baseline LDL levels are drawn for each group and are subsequently measured every 3 months for 1 year. Average baseline LDL levels for each group were identical. The group receiving statin A exhibited an 11 mg/dL greater reduction in LDL in comparison to the statin B group. Your statistical analysis reports a p-value of 0.052. Which of the following best describes the meaning of this p-value? Review Topic

QID: 104026
1

There is a 95% chance that the difference in reduction of LDL observed reflects a real difference between the two groups

24%

(12/50)

2

There is a 5% chance of observing a difference in reduction of LDL of 11 mg/dL or greater even if the two medications have identical effects

20%

(10/50)

3

Though A is more effective than B, there is a 5% chance the difference in reduction of LDL between the two groups is due to chance

36%

(18/50)

4

This is a statistically significant result

12%

(6/50)

5

If 100 permutations of this experiment were conducted, 5 of them would show similar results to those described above

2%

(1/50)

M1

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PREFERRED RESPONSE 2
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(M1.ST.77) A grant reviewer at the National Institutes of Health is determining which of two studies investigating the effects of gastric bypass surgery on fasting blood sugar to fund. Study A is spearheaded by a world renowned surgeon, is a multi-center study planning to enroll 50 patients at each of 5 different sites, and is single-blinded. Study B plans to enroll 300 patients from a single site and will be double-blinded by virtue of a sham surgery for the control group. The studies both plan to use a t-test, and they both report identical expected treatment effect sizes and variance. If the reviewer were interested only in which trial has the higher power, which proposal should he fund? Review Topic

QID: 103894
1

Study A, because it has a superior surgeon

0%

(0/26)

2

Study A, because it is a multi-center trial

15%

(4/26)

3

Study B, because it has a larger sample size

35%

(9/26)

4

Study B, because it is double blinded

23%

(6/26)

5

Both studies have the same power

4%

(1/26)

M1

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PREFERRED RESPONSE 3

(M1.ST.68) You submit a paper to a prestigious journal about the effects of coffee consumption on mesothelioma risk. The first reviewer lauds your clinical and scientific acumen, but expresses concern that your study does not have adequate statistical power. Statistical power refers to which of the following? Review Topic

QID: 103885
1

The probability of detecting an association when no association exists.

15%

(3/20)

2

The probability of detecting an association when an association does exist.

75%

(15/20)

3

The probability of not detecting an association when an association does exist.

10%

(2/20)

4

The probability of not detecting an association when no association exists.

0%

(0/20)

5

The first derivative of work.

0%

(0/20)

M1

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